Atkin-Lehner |
2+ 5- 13+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
69290n |
Isogeny class |
Conductor |
69290 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1272960 |
Modular degree for the optimal curve |
Δ |
-684952771809280000 = -1 · 215 · 54 · 138 · 41 |
Discriminant |
Eigenvalues |
2+ -2 5- 1 4 13+ 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,26867,39784968] |
[a1,a2,a3,a4,a6] |
Generators |
[14:6330:1] |
Generators of the group modulo torsion |
j |
2629406039/839680000 |
j-invariant |
L |
3.3811163620634 |
L(r)(E,1)/r! |
Ω |
0.22226447231033 |
Real period |
R |
1.2676776177635 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002371 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69290p1 |
Quadratic twists by: 13 |